Wave amplitude gain within wedge waveguides through scattering by simple obstacles.

Wave confinement, e.g., in waveguides, gives rise to a huge number of distinct phenomena. Among them, amplitude gain is a recurrent and relevant effect in undulatory processes. Using a general purpose protocol to solve wave equations, the boundary wall method, we demonstrate that for relatively simple geometries, namely, a few leaky or opaque obstacles inside a θ wedge waveguide (described by the Helmholtz equation), one can obtain a considerable wave amplification in certain spatially localized regions of the system. The approach relies on an expression for the wedge waveguide exact Green's function in the case of θ=π/M (M=1,2,...), derived through the method of images allied to group theory concepts. The formula is particularly amenable to numerical calculations, greatly facilitating simulations. As an interesting by-product of the present framework, we are able to obtain the eigenstates of certain closed shapes (billiards) placed within the waveguide, as demonstrated for triangular structures. Finally, we briefly discuss possible concrete realizations for our setups in the context of matter and electromagnetic (for some particular modes and conditions) waves.

Chaotic escape of impurities and sticky orbits in toroidal plasmas.

We investigate chaotic impurity transport in toroidal fusion plasmas (tokamaks) from the point of view of passive advection of charged particles due to E×B drift motion. We use realistic tokamak profiles for electric and magnetic fields as well as toroidal rotation effects, and consider also the effects of electrostatic fluctuations due to drift instabilities on particle motion. A time-dependent one degree-of-freedom Hamiltonian system is obtained and numerically investigated through a symplectic map in a Poincaré surface of section. We show that the chaotic transport in the outer plasma region is influenced by fractal structures that are described in topological and metric point of views. Moreover, the existence of a hierarchical structure of islands-around-islands, where the particles experience the stickiness effect, is demonstrated using a recurrence-based approach.

Soliton-like structures in the spectrum and the corresponding eigenstates morphology for the quantum desymmetrized Sinai billiard.

By continuously varying certain geometric parameters γ of the totally desymmetrized quantum Sinai billiard, we study the formation of the so-called soliton-like structures in the spectra of the resulting family of systems. We present a detailed characterization of the eigenstate ψn morphologies along such structures. Usually, scarring and bouncing ball mode states are expected to fully explain the solitons. However, we show that they do not exhaust all the possibilities. States with strong resemblance to very particular solutions of the associated integrable case ( 45°- 45° right triangle) also account for the ψn's. We argue that for the emergence of the solitons, in fact, there must be an interplay between the spatial localization properties of the soliton-related ψn's and the rescaling properties of the billiards with γ. This is illustrated, e.g., by comparing the behavior of the eigenwavelengths along the solitons and the billiard size dependence on γ. Considerations on how these findings could extend to other type of billiards are also briefly addressed.